How are your automation scripts triggering the execution of your test cases? Are you using TestRunner.exe?
Are the 1000+ tests executed as a TestSuite (an .ste file)? Or are you executing them one by one?
What Coordinator/Simulator are you using to execute these tests? Are you using the Workstation internal coordinator/simulator? (Using TestRunner the internal coordinator/simulator is triggered by using the option "-cs local")
In which log are you seeing these OOM-errors? Is it in the output of the test run? Or is it in the workstation.log?
I guess I am basically trying to assess if you are adding the JVM runtime memory to the correct component. Also, for me 1GB of max JVM memory isn't really that excessive. If we tune a DevTest platform and we are sizing the Coordinators and Simulators (the components that actually execute the testcases) then we would minimally give them 2GB, if they were to run suites of 1000+ testcases we would probably assign 4GB to the simulator, and similar to the Coordinator process.
My suggestion is to identify correctly where the tests are running (local in workstation, or on server coordinator/simulator), give that component more memory, and by giving it more memory it should be able to run more then 10+ testcases in one run. Maybe not yet all of them but if you see it evolving in the right direction then at least you know you are manipulating the right parameters.
Cheers,
Danny